American Airlines has round-trip flights from Austin (AUS) to Havana (HAV) for $277 with a connection. Flights August to November. Extended weekends available.
Main cabin. Not Basic. A Carry-on bag, seat selection, and also a personal item is allowed for free on American.
Note that Cuba has additional requirements for entry. Review entry requirements at the US State Department website.
Click for more details and booking links Cheap Flights: Austin to Havana $277 r/t [August-November] – American Airlines